if m and n are integers and m=n-(2/n)-(2/n²), which of the following could be the value of m? I. -5 II. -3 III. -1

Question

if m and n are integers and m=n-(2/n)-(2/n²), which of the following could be the value of m?            I. -5 II. -3 III. -1

anonymous · Answer

I guess you are having trouble testing the choices?

anonymous · Answer

I think that it could either be m=-3 or m=-1

anonymous · Answer

you can simplify the equation to the following. $$0=n ^{3}-mn ^{2}-2n-2$$
Then you need to find what values of m will give you integer roots for the third degree polynomial.  finding third degree polynomial roots is tricky.  Maybe I have over complicated it...

anonymous · Answer

I guess you could just guess integer values of n and hope they correspond to one of the given values of m.  (hint guess n=-1 and then n=1)

anonymous · Answer

Yes, I figured out the simplification above and after a while decided the simplest thing was just to feed them into Wolfram.

There probably is some sort of by-hand procedure but I don't know it.